The best thing to do here is hike or backpack in the Great Smoky Mountains National Park. In the Smokies, if you get off the beaten trails, there are some absolutely gorgeous spots to enjoy. Also within a drive are Frozen Head State Park (note: due to budgetary cuts, this park was closed Dec. 1, 2001), Nantahala National Forest (just across the border in North Carolina), and Big South Fork National Recreation Area (up north). For you rafters and kayakers, the Ocoee River (host of the '96 Olympics), and the Nantahala are nearby as well.
Lots of trekkers pass through Knoxville on the Appalachian Trail. It's a good spot to re-stock, get a shower, and grab a bit of R&R.
Each spring/summer/fall the city has a free concert series (Thursday nights) on Market Square in the heart of downtown. Some great headliners and openers, and the atmosphere is always pure love, with food, beer, and lots of kids.
Although I wasn't here in 1982, lots of people still remember the World's Fair. Downtown still boasts the strange Sunsphere, although there's currently a lot of noisy construction in the former {'82} World's Fair Park.
Quick Tips:
Head down to the Old City (corner of Jackson and Central) for the best nightlife in town (never mind the obvious, glaring University of Tennessee ‘strip,’ except for maybe the Longbranch). Several restaurants, clubs (jazz, hip-hop, folk/bluegrass, rock, etc.-- we have tons of talented local and regional musicians), street preachers, cafes, and groovy little shops are all within a four-block grid. Lots of Knoxville history here. (I heartily recommend a black & tan at Patrick Sullivan's saloon.)
Volunteer Landing--With restaurants, fountains, riverboats, and other humble attractions, it's a relaxing space, set against the Tennessee River. (Also where I love to run.)
Ijams Nature Park--nice trails for walking or trail running, with great activities and exhibits for kids.
The Museum of Appalachia (in Norris, TN)--Another great stop for kids--lots of farm animals and rural life exhibits (check out the great musical instrument collection).
The Museum of East Tennessee History--right downtown--has its regular "East Tennesseans" exhibit as well as other temporary exhibits. It also boasts one of the best genealogy libraries in the South.
For all else, pick up a Metro Pulse (the free weekly alternative rag). It’s got the lowdown on sports, events, movies, etc.
Best Way To Get Around:
Since we live in one of Knoxville's first 'suburbs' (the funky 4th & Gill neighborhood), we walk pretty much everywhere downtown.
Knoxville is working on becoming a more bike-friendly area, but highway construction and other administrative problems always seem to get in the way. But, since there’s usually not much traffic downtown after sundown, it’s easy to cruise around the streets at night without fear of becoming road pizza.
There are plenty of taxis to be had, but you have to call them--not many to wave down.
The KAT (Knoxville Area Transit) bus system is not very good—it has weird weekend schedules and doesn’t extend to some of the best places. If you need to take it somewhere though, the routes are pretty straightforward.
And there is now a free trolley that ferries students from the UT strip down to the Old City on weekend nights.